Apple released a Security Update today and a Java update the other day. Some people have had some problem with the Security update not allowing their machine to finish rebooting after the install.
I just downloaded and installed them on our MacBook and iMac. It was seamless. But, this is why. I downloaded both updates to the desktop, but I did not install them. I restarted the machines in Safe Boot mode by holding down the Shift Key upon restart. I installed the Java update first, then the Security Update. The Security Update requires a restart. After the machines restarted everything was just fine. No problems.
If you have installed these and are having problems try restarting your machine in Safe Boot mode. It might make it work properly. Good luck.